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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 1(26), Pages 52–65 (Mi vsgtu1067)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Analysis

On two special functions, generalizing the Mittag-Leffler type function, their properties and applications

E. N. Ogorodnikov

Samara State Technical University, Samara, Russia

Abstract: Two special functions, concerning Mittag-Leffler type functions, are studied. The first is the modification of generalized Mittag–Leffler function, which was introduced by A. A. Kilbas and M. Saigo; the second is the special case of the first one. The relation of these functions with some elementary and special functions and their role in solving of Abel–Volterra integral equations is indicated. The formulas of the fractional integration and differentiation in sense of Riemann–Liouville and Kober are presented. The applications to Cauchy type problems for some linear fractional differential equations with Riemann-Liouville and Kober derivatives are noticed.

Keywords: special functions, Mittag–Leffler type function, Riemann–Liouville integral and differential operators, fractional differential and integral equations, Cauchy type problems

DOI: https://doi.org/10.14498/vsgtu1067

Full text: PDF file (1068 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.589
MSC: Primary 33E12; Secondary 26A33, 34K37
Original article submitted 20/XI/2011
revision submitted – 27/III/2012

Citation: E. N. Ogorodnikov, “On two special functions, generalizing the Mittag-Leffler type function, their properties and applications”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(26) (2012), 52–65

Citation in format AMSBIB
\Bibitem{Ogo12}
\by E.~N.~Ogorodnikov
\paper On two special functions, generalizing the~Mittag-Leffler type function, their~properties~and~applications
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 1(26)
\pages 52--65
\mathnet{http://mi.mathnet.ru/vsgtu1067}
\crossref{https://doi.org/10.14498/vsgtu1067}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. N. Ogorodnikov, “Dve spetsialnye funktsii tipa obobschennoi funktsii Mittag–Lefflera v resheniyakh integralnykh i differentsialnykh uravnenii s operatorami Rimana–Liuvillya i Kobera”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(28) (2012), 30–40  mathnet  crossref  zmath  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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